A Discrete Density Matrix Theory for Atoms¶in Strong Magnetic Fields

This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B>> Z ^4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy. Received: 20 October 2000 / Accepted: 3 November 2000     

Atoms in Strong Magnetic Fields:¶The High Field Limit at Fixed Nuclear Charge

Let E(B,Z,N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of E(B,Z,N) as B→∞ with N and Z fixed but arbitrary. It is shown that the leading term has the form (ln B)² e(Z,N), where e(Z,N) is the ground state energy of a system of N bosons with delta interactions in one dimension. This extends and refines previously known results for N= 1 on the one hand, and N,Z→∞ with B/Z ³→∞ on the other hand. Received: 9 December 1999 / Accepted: 15 February 200     

Autocorrelation Function of Hydrogen Atoms in Magnetic Fields

The autocorrelation function is an important quantity that can reflect the dynamical properties of the Rydberg wave packet and can be measured in experiments. Applying time-dependent perturbation theory and rotating wave approximation, we derive the autocorrelation function of the double-pulse laser describing the evolution of a Rydberg wave packet of hydrogen atoms in magnetic fields. The resulting expression is written as a sum of the modified Caussian terms. Each Caussian term comes from a parent semiclassical closed orbit. It provides a direct explanation and experimentally controllable measurement scheme, which allows us therefore to recognize the closed orbit and to determine its returning time in high precision.     

Quantum Spectra of Hydrogen Atoms in Various Magnetic Fields with the Closed Orbit Theory

The quantum spectra of hydrogen atoms in various magnetic fields have been calculated with the closed orbit theory.The magnitude of the magnetic field decreases from 5.96 T to 0.56 T with a step of 0.6T.We demonstrate schematically that the closed orbits disappear with the decrease of the magnitude of the magnetic field when the corresponding finite resolution of experiment is fixed.This may give us a good way to control the shape and the number of the closed orbits in the system,and thus to control where a peak should exist in the Fourier transformation of the quantum spectra.     

Semiclassical Calculations of Recurrence Spectra for Lithium Atoms in Parallel Electric and Magnetic Fields

By using the region-splitting consistent and iterative method,we calculate the recurrence spectra of lithium atoms in parallel strong external electric and magnetic fields,and obtain the novel resonance structure in the photoabsorption spectrum above the ionization threshold with a constant scaled electric field at F=0.036,and a scaled energy at ε＝0.58 and ε=0.006,respectively.The results are compared with those of hydrogen obtained by using standard closed orbit theory.It is demonstrated that the core-scattered effects exhibited in combination recurrence play a great role.     

On the Existence of Force-Free Magnetic Fields¶with Small Nonconstant α in Exterior Domains

The existence of force-free magnetic fields in the exterior domain of some compact simply connected surface S is proved via an iteration scheme. The iteration starts with an arbitrary exterior vacuum field, which contains flux tubes originating and ending on S. At one cross-section of such a flux tube with S an arbitrary function α is prescribed. For small values of α (in the H?lder-norm 1, λ; 0 < λ < 1) the iteration is shown to converge to a force-free field with the prescribed values of α in a flux tube which is close to the vacuum flux tube and α≡ 0 outside. The force-free field is close (in the H?lder- norm 1,λ) to the starting vacuum field, in particular, it has the same field line topology, the same boundary values on S and satisfies the same decay conditions in spatial infinity. It is in general three-dimensional and requires no continuous symmetries. Received: 20 June 1999 / Accepted: 25 October 1999     

Possible Origin of Magnetic Fields in Very Dense Stars

We discuss the bosonization of a relativistic very dense Fermi gas in a magnetic field and the consequent BoseEinstein condensation of the resulting relativistic vector gas of charged particles. The model may be applied to paired spin-up electrons. We show that such systems may maintain self-consistently magnetic fields of order 10^10 - 10^13 G. That pairing could be the origin of large magnetic fields in some white dwarfs and neutron stars.For fields large enough (- 10^13 for white dwarfs), the system becomes unstable and collapses.     

The Local Structure of Zero Mode¶Producing Magnetic Potentials

We consider the class of continuous magnetic potentials on ?³ which decay as o(|x|^{? 1}). Within this class it is shown that the set of potentials whose associated Weyl-Dirac operator produces zero modes with multiplicity m forms a smooth submanifold of co-dimension m ² when m= 0, 1, 2, and is contained in a smooth submanifold of co-dimension 2m? 1 when m≥ 3.     

Optical Conductivity of Anisotropic Quantum Dots in Magnetic Fields

Optical conductivity of anisotropic double-parabolic quantum dots is investigated with the memory-function approach, and the analytic expression for the optical conductivity is derived. With characteristic parameters pertaining to GaAs, the numerical results are presented. It is shown that: (1) the larger the optical phonon frequency wLO, the stronger the peak intensity of the optical conductivity, and the more asymmetric the shape of the optical conductivity; (2) the magnetic field enhances the optical conductivity for levels l=0 and l=1,with or without electron-LO-phonon interactions; (3) the larger the quantum dot thickness lz, the smaller the optical conductivity σ(w).     

The Discrete Spectrum¶of the Perturbed Periodic Schrödinger Operator¶in the Large Coupling Constant Limit

Let A be a periodic Schr?dinger operator and let V ₀≥ 0 be a decaying potential. We study the number of the eigenvalues of the operator A(α) =A−αV ₀ inside a fixed interval (λ₁,λ₂). We obtain an asymptotic formula for as α→∞. Received: 12 September 2000 / Accepted: 22 November 2000     

Interference Dynamics of Hydrogen Atoms in High—Frequency Dichromatic Laser Fields

We investigate the ionization and high-order harmonic generation of a hydrogen atom in high-frequency (several atomic units) super strong (up to several tens of atomic units) dichromatic laser fields.An effective iterative method in the framework of high-frequency Floquet theory is used in the calculations.We have considered two kinds of dichromatic laser field,i.e.1ω-2ω and 1ω-3ω.We find that,in both the cases,the ionization and high-order harmonic generation show evident dependence on the relative phase and strength of the additional harmonic field.The dynamical origin of these interference effects is also discussed.     

“Wall Viscosity” of Magnetic Fluid Oscillations in a Strong Magnetic Field

Russian Physics Journal - The authors provide an estimation of the “wall viscosity” and its increment (“magneto-viscous” effect) in a thin near-wall layer of a column of...     

Spectral Gaps for Periodic Schrödinger Operators with Strong Magnetic Fields

We consider Schrödinger operators H^h=(ihd+A)*(ihd+A) with the periodic magnetic field B=dA on covering spaces of compact manifolds. Using methods of a paper by Kordyukov, Mathai and Shubin [14], we prove that, under some assumptions on B, there are in arbitrarily large number of gaps in the spectrum of these operators in the semiclassical limit of the strong magnetic field h0.Acknowledgement I am very thankful to Bernard Helffer for bringing these problems to my attention and useful discussions and to Mikhail Shubin for his comments.     

Magnetic Fields in Active Late—Type Stars

The very high resolution and high signal-to-noise ratio spectra of ten x-ray selected stars are obtained by the NAOC Coude spectropraph.Magnetic field measurements of these stars have been performed using the profileaddition technique.The magnetic field strength and filling factor are obtained,and we find that there exist strong magnetic fields on very active stars.     

Development of the Fast Ionization Gauge in a Strong Magnetic Field

The neutral gas pressure near plasma or divertor plates are very important for the plasma-wall interaction, which determines the operating mode of divertor and confining performances of plasma in tokamaks. A fast ionization gauge (fast gauge) is designed for this purpose in the HL-2A tokamak.     

Study on Non-Sequential Double Ionization of Aligned Diatomic Molecules in Strong Laser Fields

We develop a semiclassical model to describe the non-sequential double ionization of aligned diatomic molecules in an intense linearly polarized field. It is found that in the tunnelling regime, the oriented molecule shows geometric effects on double ionization process when aligned parallel and perpendicular to the external field. Our results are qualitatively consistent with the recent experimental observations.     

“Unmoved” Atomic Transitions of Alkali Metals in External Magnetic Fields

Journal of Experimental and Theoretical Physics - The “mixing” of magnetic sublevels of the ground and excited levels of an atomic transition with magnetic sublevels of a nearby...